Problem: Which of these numbers is prime? ${34,\ 39,\ 55,\ 59,\ 75}$
Solution: A prime number has exactly two factors: 1 and itself. The factors of 34 are 1, 2, 17, and 34. The factors of 39 are 1, 3, 13, and 39. The factors of 55 are 1, 5, 11, and 55. The factors of 59 are 1 and 59. The factors of 75 are 1, 3, 5, 15, 25, and 75. Thus, 59 is a prime number.